To find the force of air resistance acting on the paratrooper, we can use the equation F(sub)d = bv^2, where b = 0.14 N*s/m^2 and v = 64 m/s.
a) The force of air resistance can be calculated by plugging in the values into the equation:
F(sub)d = 0.14 * (64)^2
F(sub)d = 0.14 * 4096
F(sub)d = 573.44 N
Therefore, the force of air resistance acting on the paratrooper is 573.44 N.
b) To find the acceleration, we need to use Newton's second law: F = ma, where F is the net force acting on the paratrooper, m is the mass of the paratrooper, and a is the acceleration.
Since there are two forces acting on the paratrooper - the force of gravity (mg) and the force of air resistance (F(sub)d), the net force can be written as:
F(net) = F(sub)d - mg
Substituting the given values:
F(net) = 573.44 N - (120 kg * 9.8 m/s^2)
F(net) = 573.44 N - 1176 N
F(net) = -602.56 N
Since the net force is negative, it means the force of gravity is greater than the force of air resistance. Therefore, the acceleration will be in the upward direction (opposite to the direction of motion).
Using F = ma, we can rearrange the equation to solve for acceleration:
a = F(net) / m
a = -602.56 N / 120 kg
a = -5.021 m/s^2
Therefore, the acceleration of the paratrooper is approximately -5.021 m/s^2.
c) To find the terminal velocity, we need to equate the force of air resistance to the force of gravity (mg). At terminal velocity, the net force is zero (F(net) = 0), and the paratrooper stops accelerating.
Setting F(net) = 0:
F(sub)d - mg = 0
0.14v^2 - (120 kg * 9.8 m/s^2) = 0
Solving for v:
0.14v^2 = 1176
v^2 = 1176 / 0.14
v^2 = 8400
v = sqrt(8400)
v ≈ 91.65 m/s
Therefore, the terminal velocity of the paratrooper is approximately 91.65 m/s.